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Algebraic density property of Danilov–Gizatullin surfaces

Algebraic density property of Danilov–Gizatullin surfaces A Danilov–Gizatullin surface is an affine surface V which is the complement of an ample section S for the ruling of a Hirzebruch surface. The remarkable theorem of Danilov and Gizatullin states that the isomorphism class of V depends only on the self-intersection number (S.S). In this paper we apply the theorem of Danilov–Gizatullin to prove that the Lie algebra generated by the complete algebraic vector fields on V coincides with the set of all algebraic vector fields of V. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Mathematische Zeitschrift Springer Journals

Algebraic density property of Danilov–Gizatullin surfaces

Mathematische Zeitschrift , Volume 272 (4) – Feb 4, 2012

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References (28)

Publisher
Springer Journals
Copyright
Copyright © 2012 by Springer-Verlag
Subject
Mathematics; Mathematics, general
ISSN
0025-5874
eISSN
1432-1823
DOI
10.1007/s00209-012-0982-3
Publisher site
See Article on Publisher Site

Abstract

A Danilov–Gizatullin surface is an affine surface V which is the complement of an ample section S for the ruling of a Hirzebruch surface. The remarkable theorem of Danilov and Gizatullin states that the isomorphism class of V depends only on the self-intersection number (S.S). In this paper we apply the theorem of Danilov–Gizatullin to prove that the Lie algebra generated by the complete algebraic vector fields on V coincides with the set of all algebraic vector fields of V.

Journal

Mathematische ZeitschriftSpringer Journals

Published: Feb 4, 2012

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